Question

find the area of the given figure​

Answer 1

Topic :-

Mensuration

To Find :-

Area of given figure.

Steps :-

• Calculate area of rectangle RSTU.

• Calculate area of parallelogram QRUV.

• Calculate area of trapezium PQVW.

• Sum all calculated areas to obtain area of whole figure.

Formulae to be used :-

Area of rectangle = Length × Breadth

Area of parallelogram = Base × Height

Area of Trapezium =

[ ( Sum of parallel sides ) × Height ] / 2

Solution :-

Calculating area of rectangle RSTU.

• Length = 18 units

• Breadth = 6 units

Area = Length × Breadth

Area = 18 × 6 square units

Area = 108 sq. units

Calculating area of parallelogram QRUV.

• Base = 18 units, as opposite sides of rectangle are equal.

• Height = 9 units

Area = Base × Height

Area = 18 × 9 sq. units

Area = 162 sq. units

Calculating area of trapezium PQVW.

• Parallel sides = 36 units and 18 units as opposite sides of parallelogram are equal.

• Height = 9 units

Area =

[ (Sum of parallel sides) × Height ] / 2

[ ( 36 + 18 ) × 9 ] /2

[ 54 × 9 ] / 2 sq. units

486 / 2 sq. units

243 sq. units

Now,

Sum of all calculated areas = Area of given figure

Area of given figure = 108 + 162 + 243 sq. units

Area of given figure = 513 sq. units

Answer :-

So, the area of given figure is 513 square units.

Answer 2

Answer:-

Given:

▪︎A Figure PSTW in which;

▪︎A rectangle SRVT :

• length = 18

• breadth = 6

▪︎A parallelogram QRVW :

• Base = length of rectangle = 18

• Height = 9

▪︎A trapezium QWVP:

• 1st parallel side = 36

• 2nd parallel side = base of parallelogram = 18

• Height = 9

To Find:

▪︎Area of whole figure PSTW

Solution:

☆Area of figure PSTW

= Area of rectangle SRVT + Area of parallelogram QRVW + Area of trapezium QVWP

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➡️Area of rectangle SRVT

= length × breadth

= 18 × 6

= 108 units²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➡️Area of parallelogram QRVW

= Base × Height

= 18 × 9

= 162 units²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➡️Area of trapezium QVWP

= [(Sum of parallel sides) ÷ 2] × Height

= [(36 + 18) ÷ 2] × 9

= [54 ÷ 2] × 9

= 27 × 9

= 243 units²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Hence ,

Area of whole figure

= (108 + 162 + 243)units²

= 513 units²

Formula to be remembered:-

▪︎Area of rectangle = length × breadth

▪︎Area of square = Side × Side

▪︎Area of parallelogram = Base × Height

▪︎Area of trapezium = [(Sum of parallel sides) ÷ 2] × Height

▪︎Area of triangle = ½ × base × height

Or by Heron's Formula